Abstract:This paper is concerned with the Hawkins random sieve which is a probabilistic analogue of the sieve of Eratosthenes. Analogues of the prime number theorem and Mertens’ theorem have previously been obtained for this sieve by classical probabilistic methods. In the present paper, sharper results akin to the Riemann hypothesis are obtained by a more elegant martingale approach.
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- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 56 (1976), 277-280
- MSC: Primary 10H30
- DOI: https://doi.org/10.1090/S0002-9939-1976-0404177-X
- MathSciNet review: 0404177